Let \(\mathcal {L}^2 (M_X)\)  be the space of predictable functions \(\phi : \Omega \times [0,T] \times \mathbb {R}^d \rightarrow \mathbb {R}\)  such thatThis space coincides with the space \(\mathcal {P}_M\)  in [1]}. Therefore the stochastic integral with respect to the martingale measure \(M_X\)  is well defined for all \(\phi \in \mathcal {L}^2(M_X)\) .
\(\Vert  \phi \Vert _{\mathcal {L}^2(M_X)}^2 = \mathbb {E} \left[ \int _0^T \int _{\mathbb {R}^d} \phi ^2(s,x) X(s) (dx)ds \right] < \infty ,\) 
